Results 51 to 60 of about 1,131 (79)

Multipeakons and a theorem of Stieltjes

, 1999
A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions.
Beals R, Camassa R, D H Sattinger, J Szmigielski, Krein M G, R Beals, Stieltjes T J   +6 more
core   +2 more sources

Decay Rate on the Radius of Spatial Analyticity to Solutions for the Modified Camassa–Holm Equation

Journal of Mathematics, Volume 2025, Issue 1, 2025.
The initial value problem associated with the modified Camassa–Holm equation for initial data u0(x) that is analytic on the line and having uniform radius of spatial analyticity σ0 is considered. We have shown the persistence of the radius of spatial analyticity till some time δ.
Tegegne Getachew, Yongqiang Fu
wiley   +1 more source

Analytical solutions of cylindrical and spherical dust ion-acoustic solitary waves

Results in Physics, 2019
In the present work, employing the conventional reductive perturbation method to the field equations of an unmagnetized dusty plasma consisting of inertial ions, Boltzmann electrons and stationary dust particles in the nonplanar geometry we derived ...
Essam. R. El-Zahar, Hilmi Demiray
doaj   +1 more source

Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System

, 2010
In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \rho_{t}+k_{2}u\rho_{x}+(k_{1}+k_{2})\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\rho\rho_{x}=0. By the separation method,
Camassa, Deng, Escher, Goldreich, Guan, Guo, Ivanov, Jin, Lakin, Li, Liu, Makino, Manwai Yuen, Popowicz, Yuen, Yuen, Yuen, Yuen, Yuen, Zhou   +19 more
core   +1 more source

The initial-value problem for a Gardner-type equation

Advanced Nonlinear Studies
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry, Chen Hongqiu, Guerrero Pamela, Haidau Cristina, Pantic Sanja   +4 more
doaj   +1 more source

Soliton equations: admitted solutions and invariances via B\"acklund transformations [PDF]

Open Communications in Nonlinear Mathematical Physics
A couple of applications of B\"acklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evolution equations.
Sandra Carillo, Cornelia Schiebold
doaj   +1 more source

Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation

Advances in Nonlinear Analysis
In this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect.
Moon Byungsoo, Yang Chao
doaj   +1 more source

Dissipative perturbations for the K(n,n) Rosenau-Hyman equation

, 2012
Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations.
Abassy, Antonova, Bertozzi, Bin, Biswas, Biswas, Biswas, Cardenas, Cooper, Cooper, Cooper, de Frutos, Dey, Drazin, Ebadi, Fernandez, Francisco R. Villatoro, Johnson, Julio Garralón, Kardashov, Kevorkian, Khare, Kivshar, Kivshar, Kovalev, Laila, Lamb, Ludu, McLaughlin, Mihaila, Olver, Pikovsky, Rosenau, Rosenau, Rosenau, Rosenau, Rosenau, Rosenau, Rus, Rus, Rus, Rus, Triki, Zhang   +43 more
core   +1 more source

Sharp local well-posedness for KP-I equations in the semilinear regime

Forum of Mathematics, Sigma
We show sharp well-posedness with analytic data-to-solution mapping in the semilinear regime for dispersion-generalized KP-I equations on $\mathbb {R}^2$ and $\mathbb {R} \times \mathbb {T}$ .
Shinya Kinoshita, Akansha Sanwal, Robert Schippa   +2 more
doaj   +1 more source

Soliton surfaces associated with symmetries of ODEs written in Lax representation

, 2011
The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs ...
A M Grundland, Briot C, Byrd P, Conte R, do Carmo M P, Grundland A M, Grundland A M, Grundland A M, Helgason S, Landau L D, S Post, Winternitz P   +11 more
core   +1 more source